Algorithms and Complexity

Theoretical Computer Science - Bridging Course
Graduate Course - Winter Term 2018/19
Fabian Kuhn


Exam Review

The exam review will be on 17th April from 2 pm to 3 pm in room 106-00-015.

Course description

The aim of the course is to provide basic knowledge of theoretical computer science to computer science M.Sc. students who do not yet have this necessary background (e.g., because of a different major during their undergraduate studies). The course introduces the (mathematical) foundations of theoretical computer science. We will see what can be computed and how efficiently, as well as what cannot. More specifically, the following topics will be included:

  • Automata
  • Formal languages
  • Formal grammars
  • Turing machines
  • Decidability
  • Complexity Theory
  • Logic

Course Format

The course is based on existing recordings provided by Diego Tipaldi combined with weekly exercise lessons. This will prepare the participants for the exercise sheets that have to submitted weekly and for the final exam.


The exercise lessons will take place each Monday from 12:15 to 1:45 pm in building 101 room SR 01 016 (Georges-Koehler-Allee 101).

There will be no tutorial on 28th January. On 4th February, there will be a session for questions regarding the complete material of the course.


The exam will take place on 4th of March 2019 at 2 pm in room 101-01-009/13 (the rooms are next to each other). It will take 90 min. The exam will be an open-book exam, which means you are allowed to bring any printed or written material. Electronic equipment is not allowed!

We recommend you to write a summary of the topics covered in the lecture. This has two advantages: First, you will see the big picture and also learn the details (if your summary is well crafted and if you do it by yourself). Second you can bring it to the exam in case you can't rememeber some definition (this is way more handy than a book which you have never worked with before).

Slides and Recordings

The course is based on existing recordings provided by Diego Tipaldi.

Topic Slides Recordings
Mathematical Preliminaries PDF MP4 (44:30)
DFA, NFA, Regular Languages PDF MP4 (1:14:04)
Regular Languages and closure wrt elementary operations
Regular expressions MP4 (1:37:55)
Non-regular languages MP4 (22:12)
Context Free Grammars I PDF MP4 (1:34:09)
Context Free Grammars II MP4 (42:00)
Pushdown Automata MP4 (1:11:18)
Pumping Lemma for Context Free Grammars MP4 (1:29:51)
Turing Machines I PDF MP4 (52:31)
Turing Machines II MP4 (1:23:03)
Decidability and decidable languages. PDF MP4 (52:54)
Decidability, mathematical backgrounds on cardinality, Cantor's diagonal argument MP4 (1:15:40)
Decidability and the halting problems. MP4 (12:50)
Complexity I PDF MP4 (1:28:51)
Complexity II MP4 (1:34:27)
Complexity III MP4 (1:28:08)
Propositional Logic and basic definitions, CNF/DNF, logical entailment. PDF MP4 (37:11)
Propositional Logic. Deduction/Contraposition/Contradiction Theorems and Derivations. MP4 (1:00:14)
Propositional Logic. Derivations, Soundness and Completeness of calculi. MP4 (53:16)
Propositional Logic. Refutation-completeness and Resolution. MP4 (04:16)
First Order Logic. Derivations. PDF MP4 (46:47)
First Order Logic. Satisfaction, closed formulae and brief overview on Normal Forms. MP4 (1:39:04)


Submit your solutions by sending an E-mail to philipp.bamberger(at)cs.uni-freiburg.de or bring your solution as hard copy to the exercise lessons.

Week Topic(s) Assigned Date Due Date Exercises Sample Solution

1 Mathematical Preliminaries 22.10.2018 29.10.2018 Exercise 01 Solution 01
2 Automata, Regular Languages 29.10.2018 05.11.2018 Exercise 02 Solution 02
3 Regular Expressions, Pumping Lemma, ContextFree Grammar 05.11.2018 12.11.2018 Exercise 03 Solution 03
4 PDA, Chomsky Normal Form, Context Free Grammar 12.11.2017 19.11.2017 Exercise 04 Solution 04
5 Turing Machines 19.11.2018 26.11.2018 Exercise 05 Solution 05
6 Decidability 26.11.2018 03.12.2018 Exercise 06 Solution 06
7 Decidability, Landau Notation 03.12.2018 10.12.2018 Exercise 07 Solution 07
8 Decidability, P, NP 10.12.2018 17.12.2018 Exercise 08 Solution 08
9 P vs. NP 17.12.2017 07.01.2018 Exercise 09 Solution 09
10 Propositional Logic, CNF, DNF, Calculi 07.01.2019 14.01.2019 Exercise 10 Solution 10
11 FO Logic, Resolution Calculus 14.01.2019 21.01.2019 Exercise 11 Solution 11

Additional Material

Previous Exams (no sample solutions are provided)

Text Books

[sipser] Introduction to the Theory of Computation
Michael Sipser
PWS Publishing, 1997, ISBN 0-534-95097-3
[HMU] Introduction to Automata Theory, Languages, and Computation
John E. Hopcroft, Rajeev Motwani, Jeffrey D. Ullman
Addison-Wesley, 3rd edition, 2006, ISBN 81-7808-347-7
[mendelson] Introduction to Mathematical Logic
Elliott Mendelson
CRC Press, 6th edition, 2015, ISBN-13: 978-1482237726
[enderton] A Mathematical Introduction to Logic
Herbert B. Enderton
Academic Press, 2nd edition, 2001, ISBN-13: 978-0122384523


There is an error on page 35 of the second set of the lecture slides on which the pumping lemma is stated. The statement should be made about strings s of length at least p from the language A (instead of any string s of length at least p).